Problem: $ A = \left[\begin{array}{rrr}6 & 9 & 1 \\ 4 & 0 & 5 \\ 6 & 7 & 9\end{array}\right]$ What is $ A^{T}$ ?
Solution: To find the transpose, swap the rows and columns. $ A^{T}$ = $\left[\begin{array}{rrr}6 & 4 & 6 \\ 9 & 0 & 7 \\ 1 & 5 & 9\end{array}\right]$